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SIGMA 3 (2007), 078, 20 pages math.QA/0604158
https://doi.org/10.3842/SIGMA.2007.078
Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn
Wakako Nakai and Tomoki Nakanishi
Graduate School of Mathematics,
Nagoya University, Nagoya 464-8602, Japan
Received May 03, 2007, in final form July 04, 2007; Published online July 18, 2007
Abstract
We study the Jacobi-Trudi-type determinant which is conjectured to be
the q-character of a certain, in many cases irreducible, finite-dimensional
representation of the quantum affine algebra of type Cn.
Like the Dn case studied by the authors recently,
applying the Gessel-Viennot path method with
an additional involution
and a deformation of paths, we obtain an expression by a positive sum over
a set of tuples of paths,
which is naturally translated into the one over a set of tableaux
on a skew diagram.
Key words:
quantum group; q-character; lattice path; Young tableau.
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